Fibonacci Sequence/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. Tim, a boy, and his robot friend Moby are walking through a field. They come upon a white rabbit. Another rabbit shows up, and then a third. TIM: Wow, looks like it’s rabbit season. Moby beeps and seizes Tim’s shoulders. TIM: No, no, not for hunting! I just meant there’re a lot of rabbits here. Tim pulls a letter from his pocket. Text reads as Tim narrates: Dear Tim & Moby; I just saw a movie that talked about Fibonacci numbers, but I still don’t get what they are. Can you help me? From, Jordi. TIM: Hey, good question! The Fibonacci numbers are a sequence of numbers that all have a very specific relationship to each other. Two labels appear, reading, Fibonacci numbers, and, sequence. A series of numbers appears, reading, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55. TIM: In math, a sequence is basically a list of numbers arranged in a particular order. So like if you wanted to talk about the sequence of whole numbers, it goes 0, 1, 2, 3, 4, 5, 6… A label appears, reading, whole numbers. The following numbers appear: 0, 1, 2, 3, 4, 5, and 6. Moby beeps. TIM: Yeah, okay, you get it. Sometimes sequences are a little more complicated, though. The Fibonacci sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. A label appears, reading, Fibonacci numbers. The following numbers appear: 0, 1, 1, 3, 5, 8, 13, 21, 34, and 55. TIM: Hey, can you figure out why it’s those numbers and not any others? Moby does some math on his arm calculator and is stumped. He beeps. TIM: These are all numbers you get by adding the previous two numbers, starting with 0 and 1. So 0 plus 1 is 1; 1 plus 1 is 2; 1 plus 2 is 3; 2 plus 3 is five; and so on. Onscreen, 0 and 1, the first two numbers in the Fibonacci sequence are added together. Their sum creates the third number in the sequence, 1. Next, the second two numbers in the sequence, 1 and 1, are added together. They sum up to the third number in the sequence, 2. The formula repeats through the next two successive pairs in the sequence. Moby beeps. TIM: Well, it’s named after a mathematician called Leonardo da Pisa. Onscreen, Leonardo da Pisa appears. A label reads, Leonardo da Pisa. TIM: Leonardo was from Pisa, Italy, where the famous leaning tower is. Onscreen, a map of Italy appears. A dot in the northwest part of the country marks the city of Pisa. The dot expands to show an image of the Leaning Tower of Pisa. Moby beeps. TIM: Nope, nope. Different guy. You’re thinking of Leonardo da Vinci. He was born about 200 years after our Leonardo died. Onscreen, Leonardo da Vinci appears. He is imagining the design of a primitive helicopter. TIM: Leonardo da Pisa was better known as Fibonacci, which in Latin translates to, Son of Bonaccio. Fibonacci was one of the first Europeans to use the Arabic number system, with the digits 0 through 9. Onscreen, the numbers 0 through 9 appear. A label reads, Arabic numerals. TIM: Before that, Europeans used Roman numerals. Onscreen, the Roman numerals for 1 through 10 appear. A label reads, Roman numerals. Moby beeps. TIM: Oh, right, the rabbits. Well, in his book Liber Abaci, Fibonacci posed the following problem. Onscreen, a book appears, titled Liber Abaci, or Book of Calculation, by Leonardo da Pisa. TIM: Imagine you have a pair of baby rabbits, a male and a female. Onscreen, two rabbits appear. TIM: Now, let’s say that the rabbits mature after one month and mate. Onscreen, the rabbits look at each other, and a large red heart fills the screen. TIM: After a onemonth pregnancy, the female gives birth to one male and one female bunny. Onscreen, a chart made of horizontal rows appears. The rows are marked Month 1, Month 2, and Month 3. As Tim speaks, the chart is filled in with rabbit heads. Month 1 contains one pair of baby rabbit heads. Month 2 also contains one pair of adult rabbit heads. Month 3 contains one pair of adult rabbit heads, and one pair of baby rabbit heads. TIM: And those baby rabbits behave exactly as their parents, maturing after one month, and giving birth to a male and female bunny after one month. Onscreen, a pair of rabbits looks at each other, and a large heart fills the screen. TIM: Assuming all the rabbits survive, how many pairs of rabbits would you have after one year? Moby beeps. Many more bunnies are hopping around in the field. TIM: Yeah, it’s definitely a lot of rabbits! You start off with one pair. Onscreen, rows for month 4 and month 5 appear in the chart. A column at the right indicates the number of rabbit pairs in each row. TIM: At the beginning of the second month, the rabbits have just mated, so there’s still just one pair. At the start of the third month you have two pairs: the original and the new pair. The original pair mates again, so at the beginning of the fourth month, they give birth to a second pair, making three pairs in all. Onscreen, Month 4 now contains three pairs of rabbit heads. TIM: At that point, both the original pair and their first set of children mate, so two new pairs are born at the beginning of the fifth month, making five pairs in all. And so on. Onscreen, Month 5 now contains five pairs of rabbit heads. TIM: Fibonacci probably didn’t invent the rabbit problem, but he made it so popular that it eventually became associated with him and the number sequence that now bears his name. Moby beeps. TIM: See, that’s the strange part. The Fibonacci sequence has this tendency to show up in nature, much more often than you’d think. Onscreen, a bird circles above a mountain landscape. TIM: What might seem like a simple mathematical game actually kinda describes a part of the underlying logic of the universe! Onscreen, a spiral galaxy rotates in outer space. TIM: If you look at a flower, chances are that the number of petals it has is a Fibonacci number! Onscreen, four flowers appear: one with three petals, one with five petals, one with eight petals, and one with 13 petals. TIM: And pine cones and sunflower heads have spiral patterns that are grouped in Fibonacci numbers. Onscreen, a pinecone appears. 13 rows of seeds form a spiral radiating out from the center. Moby beeps. TIM: Well, don’t get too carried away. You might have heard that the Fibonacci numbers have been used to create music, art, and architecture. For instance, people have said Leonardo da Vinci used the numbers to create the proportions in his paintings. Onscreen, da Vinci's artwork appears: his portrait of Mona Lisa, and his drawing of the Vitruvian Man. TIM: And places like the United Nations Secretariat building and the Parthenon are thought to have been designed with the Fibonacci numbers in mind. Onscreen, two buildings appear: the United Nations Building in New York City, and the Parthenon in Athens. TIM: Mostly, though, these are just myths. Moby beeps. TIM: Hey, that doesn’t make the Fibonacci sequence any less cool. Oh, by the way, the answer to that rabbit riddle is 144. After one year, that first pair will have turned into 144 pairs of wabbits…er, rabbits. Isn’t that cool? Moby? Onscreen, Tim turns to find Moby covered up to his eyeballs in a pile of rabbits. Moby gives a muffled beep. Category:BrainPOP Transcripts Category:BrainPOP Math Transcripts